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Sur une équation elliptique non linéaire dégénérée

Abstract : This work deals with the existence and the uniqueness of the solution for a degenerated nonlinear elliptic equation, posed in an unbounded domain. In a first time, using truncation technique, we reduce the study to a bounded domain. In the first part, we introduce the associated variational problem exprimed as a noncoercive integral functional which has to be minimized. We introduce then a dual problem associated to the initial problem and we prove for this last the existence and the uniqueness of the solution. Thus, we establish by extracting a minimizing subsequence the existence of a "solution" related to that of the dual problem. In the second part, we define a relaxed problem having the same infimum that the initial problem and we prove that this infimum is actually a minimum for the relaxed problem. Next, the results of the first part are extended to the unbounded case. We give then some criterion to estimate the truncated error between the solutions for the dual problem defined in the bounded and unbounded case.
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https://tel.archives-ouvertes.fr/tel-00002263
Contributor : Amira Obeid-El Hamidi <>
Submitted on : Wednesday, February 19, 2003 - 12:06:37 PM
Last modification on : Tuesday, February 2, 2021 - 2:54:04 PM
Long-term archiving on: : Wednesday, November 23, 2016 - 3:32:03 PM

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  • HAL Id : tel-00002263, version 2

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Amira Obeid-El Hamidi. Sur une équation elliptique non linéaire dégénérée. Mathématiques [math]. Université de Pau et des Pays de l'Adour, 2002. Français. ⟨tel-00002263v2⟩

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